How the CMB
challenges
cosmology’s
standard model
Glenn D. Starkman
Craig Copi, Dragan Huterer & Dominik Schwarz
Francesc Ferrer, Amanda Yoho
Neil Cornish, David Spergel, & Eiichiro Komatsu
Pascal Vaudrevange,, Dan Cumberbatch;
Jean-Philippe Uzan, Alain Riazuelo, Jeff Weeks,
R. Trotta, Pascal Vaudrevange,
Bob Nichols, Peter Freeman
Joe Silk, Andrew Jaffe, Anastasia Anarchiou
COBE - DMR
The WMAP Sky
NASA/WMAP Science team
Outline
The largest scale properties of the universe:

the angular power spectrum Cl
The low-l / large-angle problem

from Cl to C()
Beyond Cl and C()
•
seeing the solar system in the microwave background
And back:
troubles in cosmological paradise
The WMAP Sky
NASA/WMAP Science team
Angular Power Spectrum
T = lmalm Ylm(,)
T
=

a
Y
(,)
m
m
m
l
l
l
C = (2l+1)  |a |
l
-1
m
lm
2
Standard model for the origin of fluctuations (inflation):
alm are independent Gaussian random variables,
6 parameter fit to ~38 points
with < alm al’m’> = Cl l l ‘mm’
Sky is statistically isotropic and Gaussian random
ALL interesting information in the sky is contained
in Cl
Cl = (2l+1)-1m |alm|2
NASA/WMAP Science team
Measuring the shape of space
NASA/WMAP Science team
Cosmic Triangle
Angular Power Spectrum
 0x
Is there anything interesting
left to learn about the
Universe on large scales?
Motivation:
“The Low-l Anomaly”
The microwave background in a
“small” universe
Absence of long wavelength modes 
Absence of large angle correlations
Measuring the shape of space
Three Torus
Same idea works in three space dimensions
Infinite number of tiling patterns
This one only works in hyperbolic space
Spherical Topologies
This example only works in
spherical space
The microwave background in a
multi-connected universe
figure: J. Shapiro-Key
N. Cornish, D. Spergel, GDS gr-qc/9602039, astro-ph/9708083,
astro-ph/9708225, astro-ph/9801212
Matched circles in a three torus
universe
Matched Circles in
Simulations
In a blind test >99%
of circles found in a
“deliberately difficult”
universe
Searching the WMAP Sky:
antipodal circles
Single 95% C.L threshold
Circle statistic on WMAP sky
Implications
• No antipodal matched circles larger than
25o at > 99% confidence
• now extended to 20o by pre-filtering.
• Unpublished: no matched circles > 25o.
• Universe is >90% of the LSS diameter
(~78Gyr) across (Vcell>75% VLSS)
• Search is being repeated on 5-year data
• Sensitivity should improve to 10o-15o
If there is topology, it’s beyond
(or nearly beyond) the horizon
Beyond Cl:
Searches for Departures from
Gaussianity/Statistical Isotropy
• angular momentum dispersion axes (da Oliveira-Costa, et al.)
• Genus curves (Park)
• Spherical Mexican-hat wavelets (Vielva et al.)
• Bispectrum (Souradeep et al.)
• North-South asymmetries in multipoint functions
(Eriksen et al., Hansen et al.)
• Cold hot spots, hot cold spots (Larson and Wandelt)
• Land & Magueijo scalars/vectors
• multipole vectors
(Copi, Huterer & GDS; Schwarz, SCH; CHSS;
also Weeks; Seljak and Slosar; Dennis)
Multipole Vectors
Q: What are the directions associated
with the l th multipole:
Tl () m almYlm () 
Dipole (l =1) :
m a1mY1m () 
A() (ûx(1,1), ûy(1,1), ûz(1,1)) (sin cos, sin sin, cos)
Advantages: 1) û (1,1) is a vector, A() is a scalar
2) Only A() depends on C1
Multipole Vectors
General l, write:
m almYlm ()
A(l) (û (l,1)ê)…(û (l, l) ê ) - all traces]
{{alm, m=- l,…, l}, l =(0,1,)2,…} 
l
(
{A )
l
(
{û ,i),
l =1,… l}, l = (0,1,)2,…}
l
l
(
,i)
(
Advantages: 1) û are vectors, A ) is a scalar
l
2) Only A( ) depends on Cl
Maxwell Multipole Vectors
(l,1)
(l,
l)
m almYlm ()  (u
)… (u
)r -1]r=1
manifestly symmetric AND trace free:
2 (1/r)  (r)
J.C. Maxwell, A Treatise on Electricity and Magnetism, v.1, 1873 (1st ed.)
Notice:
•
•
Area Vectors
Quadrupole has 2 vectors,
Octopole has 3 vectors,
i.e. quadrupole is a plane
i.e. octopole is 3 planes
Suggests defining:
w(l,i,j)  (û (l,i) x û (l,j)) “area vectors”
Carry some, but not all, of the information
For the experts:
• w(2,2,2) || n2
• octopole is perfectly planar if w(3,1,2) || w(3,2,3) || w(3,3,1)
and then: n3 || w(3,I,j)
l=2&3 Area Vectors
l=3 normal
l=2 normal
l=3 normal
equinox
l=2
normal
dipole
l=3 normal
l=3 normal
dipole
equinox
l=3 normal
l=3 normal
Alignment probabilities
Probability of the quadrupole and octopole planes
being so aligned:
(0.1-0.6)%
Conditional probability of the aligned planes being so
perpendicular to the plane of the solar system:
(0.2-1.7)%
Conditional probability of aligned planes perpendicular
to the solar system pointing at the dipole/ecliptic:
few%
Net : < 10-5
Area vectors tell about the orientations of
the normals of the multipole planes
DON’T include all the information
(multipole vectors do)
Can rotate the aligned planes
about their common axis!
l=2&3 : The Map
Quadrupole+Octopole
Correlations -- Explanations:
Cosmology?
• Cosmology -- you’ve got to be kidding? you choose: the dipole or the ecliptic ?
Quadrupole+Octopole
Correlations -Explanations: Systematics?
• Cosmology
• Systematics -- but …
how do you get such an effect?
esp., how do you get a N-S ecliptic asymmetry? (dipole mis-subtraction?)
how do you avoid oscillations in the time-ordered data?
possibilities -- correlation of beam asymmetry with observing pattern (S. Myer)
Angular Power Spectrum
At least 3 other major
deviations in the Cl in
1st year data
Power spectrum: ecliptic plane vs. poles
“First Year Wilkinson
Microwave Anisotropy
Probe (WMAP)
Observations:
The Angular Power
Spectrum”
G. Hinshaw, et.al., 2003,
ApJS, 148, 135 -only v.1 on archive
All 3 other
major
deviations are
in the ecliptic
polar Cl only!!
No Dip?
© Boomerang Collaboration
The case against a systematic (cont.)
Archeops
Ferrer, Starkman & Yoho (in progress): the anomaly in the first peak is (largely or
entirely) localized to a region around the north ecliptic pole representing < 10% of
the sky. Statistical significance tbd.
Quadrupole+Octopole
Correlations -Explanations: more galaxy?
• Cosmology
• Systematics
• The Galaxy:
• has the wrong multipole structure (shape)
• is likely to lead to GALACTIC not ECLIPTIC/DIPOLE/EQUINOX correlations
Quadrupole+Octopole
Correlations -Explanations: Foregrounds?
• Systematics
• Cosmology
• The Galaxy
• Foregrounds -- difficult:
1. Changing a patch of the sky typically gives you: Yl0
2. Sky has 5x more octopole than quadrupole
3. How do you get a physical ring perpendicular to the ecliptic
Caution: can add essentially arbitrary dipole, which can entirely distort the
ring! (Silk & Inoue)
4. How do you hide the foreground from detection? T≈TCMB
Future data
Dvorkin, Peiris & Hu: Planck TE cross-correlation will test models “where a
superhorizon scale modulation of the gravitational potential field causes the CMB
temperature field to locally look statistically anisotropic, even though globally the
model preserves statistical homogeneity and isotropy.
F(x) = g1(x) [1 + h(x)] + g2(x)
Where g1(x) and g2(x) are Gaussian random fields and
h(x) is the modulating long-wavelength field
For dipolar h(x), predictions for the correlation between the first 10 multipoles of the
temperature and polarization fields can typically be tested at better than the 98% CL.
For quadrupolar h, the polarization quadrupole and octopole should be moderately
aligned. Predicted correlations between temperature and polarization multipoles
out to ℓ = 5 provide testsat the ∼ 99% CL or stronger for quadrupolar models that make
the temperature alignment more than a few percent likely.
“The Low-l Anomaly”
The low
quadrupole
“The Large-Angle Anomaly”
The Angular Correlation Function,
C()
C() = < T()T()>cos
But (established lore):
C() = l Cl Pl(cos ())
 Same information as Cl, just
differently organized
IF
• C() is obtained by a full sky
average
or
• the sky is statistically isotropic,
i.e. if <alm a*l’m’>=ll’ mm’Cl
NASA/WMAP science team
Is the Large-Angle Anomaly
Significant?
One measure (WMAP1):
1/2
S1/2 = -1 [C()]2 d cos 
Only 0.15% of realizations of
inflationary CDM universe
with the best-fit parameters
have lower S!
“The Low-l Anomaly?
What Low-l Anomaly?”
Two point angular correlation
function -- WMAP1
Two point angular correlation
function -- WMAP3
Statistics of C(θ)
S1/2 = -1
1/2
[C()]2 d cos 
Origin of C(θ)
Is it an accident?
Only 2% of rotated and cut full skies
have this low a cut-sky S1/2
Origin of C(θ)
Low l = large angle?
The low-l Cl are therefore not measuring
large angle (θ~π/l ), but smaller angle
correlations
Violation of GRSI
Even if we replaced all the theoretical Cl
by their measured values up to l=20,
Translation:
The
observed
cosmic variance
would
give only absence
a 3%
chanceofoflarge-angle
recovering thiscorrelation
low an S1/2 in a
particular realization
is inconsistent
(>>97%) with the
and most of thost of those are much
most
fundamental
prediction
of
poorer fits with the theory than is the
inflationary
cosmology!
current data
(Copi, Cumberbatch, GDS in preparation)
SUMMARY
If you believe the observed full-sky CMB:
There are signs that the sky is NOT
statistically isotropic
• These
are VERY statistically significant
(>>99.9%)
• The observed low-l fluctuations appear correlated
to the solar system (but not to other directions)
SUMMARY
If you don’t believe the CMB inside the Galaxy
Is reliable then:
CMB lacks large angle correlations
• first seen by COBE (~5% probable),
• now statistically much less likely
(~.03% probable)
This lack of correlations/power could be due to:
• Statistical fluctuation -- incredibly unlikely
• Topology -- not (yet?) seen
• features in the inflaton potential -- contrived,
and << 3% chance of such low S1/2
Conclusions
We can’t trust the low-l microwave to be cosmic
=> inferred parameters may be suspect (, A, 8,…)
Removal of a foreground will likely mean
even lower C() at large angles
expect P(Swmap| Standard model)<<0.03%
Contradict predictions of
generic inflationary models
at >99.97% C.L.
While the cosmic orchestra may be
playing the inflation symphony,
somebody gave the bass and the tuba
the wrong score. They’re trying very
hard to hush it up.
There is no good explanation for any of this.
Yet.